Cardiovascular disease remains the leading cause of death in the western world, placing an ever-increasing burden on both private and public health services [“The burden of chronic diseases and their risk factors: National and state perspectives,” National center for chronic disease prevention and health promotion, Department of health and human services, Atlanta, Ga. February 2004]. The electrocardiogram-gated cardiac x-ray computed tomography (CT) imaging is a promising non-invasive technique for early detection and characterization of various signs of cardiac diseases such as fatty vulnerable soft plaque (atherosclerosis) in coronary arteries, perfusion defect in myocardial, etc [M. Gilard, J.-C. Cornily, P.-Y. Pennec, C. Joret, G. Le Gal, J. Mansourati, J.-J. Blanc, and J. Boschat, “Accuracy of Multislice Computed Tomography in the Preoperative Assessment of Coronary Disease in Patients With Aortic Valve Stenosis,” Journal of the American College of Cardiology, vol. 47, pp. 2020-2024, 2006].
There are, however, two major problems with the current cardiac technique: large radiation dose to patients and insufficient temporal resolution [K. Taguchi, W. P. Segars, G. S. K. Fung, and B. M. W. Tsui, “Toward time resolved 4D cardiac CT imaging with patient dose reduction: estimating the global heart motion,” in Medical Imaging 2006: Physics of Medical Imaging, San Diego, Calif., USA, 2006, pp. 61420J-9]. The typical radiation dose with cardiac CT is 10-15 mSv, which is 3-5 times as large as a standard chest CT scan. The current temporal resolution is merely 80-165 ms in contrast to the minimum requirement of 10-30 ms to observe the beating heart motion without motion artifact.
The current technique uses the electrocardiogram signals to select projection data acquired in a time or gating window that is placed within a cardiac cycle with relatively slow motion (e.g., mid-diastole). Images are then reconstructed by neglecting the cardiac motion within the time window, however, neglecting cardiac motion can result in blurring and artifacts in the reconstructed images. Also, this technique uses only 10-30% of the acquired projection data—the data within the cardiac time window—and throws away the rest of “off-phase” data, resulting in unnecessary radiation dose to patient if the tube current is not prospectively modulated.
A graphical representation of the current technique where a gating window is placed within a cardiac cycle (i.e., heart motion) is illustrated in FIGS. 1A, B. A graphical representation of image noise versus spatial/temporal resolution that show qualitatively that with this technique there is a trade-off made between noise and resolution is shown in FIGS. 2A, B. When the gating window is set as shown in FIG. 1A to have a relatively short duration (e.g., approximately 100 ms) with respect to the cardiac cycle, the spatial/temporal resolution is considered better, however, the image noise becomes a greater factor with regards to the grainess or sharpness of the image. If the duration of the gating window is set as illustrated in FIG. 1B so as to have a relatively long duration (e.g., approximately 300 ms) with respect to the cardiac cycle, then as shown in FIG. 2B, the spatial/temporal resolution becomes worse and image noise is less of a factor with regards to the grainess or sharpness of the image.
From the standpoint of reducing dosage, recently, a method to turn off the x-ray for the off-phase has been proposed [J. Hsieh, J. Londt, M. Vass, J. Li, X. Tang, and D. Okerlund, “Step-and-shoot data acquisition and reconstruction for cardiac x-ray computed tomography,” Medical Physics, vol. 33, pp. 4236-4248, 2006]. This method is expected to reduce the dose significantly; however, this is achieved at the expense of the functional (motion) information. IN this technique, the only projection data that would be acquired is that during the cardiac time window, which as indicated above would only represent a small percentage of the projection data which could be acquired during a complete cardiac cycle.
Image reconstruction of dynamically deforming objects from projection data and known time-dependent motion field is of interest for x-ray computed tomography (CT). Clinical applications include the imaging of the heart, lungs, and liver with the cardiac and respiratory motions. Most of the currently known methods used for x-ray CT combine a gating scheme and an analytical reconstruction method. The gating scheme, as described above, uses a gating window to extract projection data acquired within a narrow window width (e.g., 80-165 ms for cardiac imaging). The images are then reconstructed while neglecting the motion within the window width. As discussed above, these methods suffer from a tradeoff between the image noise and the spatial/temporal resolution. If the in-frame motion is not negligible, it results in motion artifacts or blurring in images. The use of a narrower gating window will improve both the temporal and spatial resolution; however, it will increase the image noise as the number of photons contributed to an image is decreased. Thus, it has been sought to develop fully four-dimensional reconstruction algorithms, which compensate the motion of the object during the reconstruction process.
Algorithms have been developed to reconstruct images of the dynamically deforming objects with known motion from projections. Crawford, et al., proposed an approximate FBP-type (ramp filtering-based) method to compensate for a special combination of translation and anisotropic scaling (expansion and contraction) for the respiratory motion [Crawford, C. R., et al., Respiratory compensation in projection imaging using a magnification and displacement model. Medical Imaging, IEEE Transactions on, 1996. 15(3): p. 327-332]. The algorithm was a ramp filtering (FBP) with a change of variables to take a global motion model into account. A few exact methods have been proposed which compensate the standard or relaxed affine transformations. Roux et al. [Roux, S., bastien, Desbat, L., Koenig, A, and Grangeat P, Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations. Physics in Medicine and Biology, 2004. 49(11): p. 2169-2182] developed an exact algorithm for a global time-dependent affine transformation by incorporating transformation operation into Noo's derivative Hilbert transform (DFBP) algorithm [Noo, F., et al., Image reconstruction from fan-beam projections on less than a short scan. Physics in Medicine and Biology, 2002. 47(14): p. 2525-2546].
Desbat, et al. extended Roux's motion model to a relaxed version of affine transformation [Desbat L., Roux S. and Grangeat P., Compensation of Some Time Dependent Deformations in Tomography, In: Noo F, Zeng G L, Kudo F editors, The 8th International meeting on fully three-dimensional image reconstruction in Radiology and Nuclear Medicine, 2005 Jul. 6-9, 2005, Salt Lake City, Utah; 2005, P. 120-32]. In these methods, the DFBP or DBPF algorithms were developed for stationary objects. With all of these methods, the image reconstruction formulae integrate the compensation of the used motion model.
Such DFBP-based affine transformation compensation algorithms DAFBP, are exact; however, the motion model is restricted such that lines (rays) remain lines even after deformation. Most of the non-rigid transforms such as respiratory or cardiac motion do not satisfy this restriction, i.e., lines become curves with deformation. For respiratory compensation, Ritchie et al. [Ritchie C J, Crawford C R, Godwin J D, King K F, Yongmin K, Correction of computed tomography motion artifacts using pixel-specific backprojection Medical imaging, IEEE Transactions on 1996; 15(3): 333-42] applied Crawford's algorithm on a local basis by changing the motion model for each pixel. Despite its global nature of the ramp filtering, the reconstructed images were in good quality demonstrating significantly reduced motion artifact.
Schafer, et al., also have proposed an empirical FBP-based method which, during the backprojection process, merely traces the motion of a point of reconstruction and select the corresponding ray passing through the point at each time t [Schafer, D., et al., Motion-compensated and gated cone beam filtered back-projection for 3-D rotational X-ray angiography. Medical Imaging, IEEE Transactions on, 2006. 25(7): p. 898-906.]. Schafer's method is based on so called direct cone-beam geometry for C-arm cardiac imaging, which has been extended to parallel-fan-beam geometry for helical cardiac CT imaging and showed promises [van Stevendaal, U., et al. Motion-compensated reconstruction in helical cardiac CT. in the 9th international conference on fully three-dimensional reconstruction in radiology and nuclear medicine. 2007. Lindau, Germany]. An image reconstructed by Schafer's method with wider gating window width (40% of the R-R interval) exhibited less motion artifact with improved sharpness than an image reconstructed by the conventional FBP method with narrower window width (22%). Schafer's method has intuitively been understood as a crude approximation.
It thus is desirable to provide new methodologies or techniques for reconstructing projection data while compensating for motion of object(s) within the field of view of the scanning or imaging apparatus. It also would be desirable for such methodologies or techniques to be adapted for use in combination with any of a number of imaging modalities as known to those skilled in the art as well as being adapted for use in reconstructing images for a wide range of items including biological tissue (e.g., hearts, livers, respiratory, muscuskeletal, brain imaging with a length scan) and non-distractive industrial scanning. It also would be desirable to provide systems, apparatuses, software code and computer readable mediums embodying such software code that embody such methodologies and techniques